How many customers to expect on any given day

A manager at an ice cream store is trying to determine how many customers to expect on any given day. Overall business has been relatively steady over the past several years, but the customer count seems to have its ups and downs. He collects data over 30 days and records the number of customers, the high temperature that day, whether the day fell on a weekend/weekday and whether or not an employee stands outside the store’s entrance and hands out free samples. Customers Temperature Day of Week Free Samples 376 75 Weekday Yes 433 78 Weekday Yes 524 80 Weekday No 360 70 Weekday No 500 80 Weekday No 645 78 Weekend No 667 80 Weekend Yes 542 85 Weekday No 412 70 Weekday No 435 72 Weekday Yes 396 69 Weekday Yes 425 70 Weekday Yes 702 90 Weekend Yes 725 85 Weekend No 509 80 Weekday Yes 450 74 Weekday No 378 70 Weekday Yes 433 69 Weekday No 467 71 Weekday Yes 679 82 Weekend No 701 80 Weekend Yes 529 83 Weekday Yes 599 92 Weekday Yes 543 90 Weekday No 432 80 Weekday Yes 375 70 Weekday Yes 690 70 Weekend No 734 85 Weekend Yes 465 74 Weekday Yes 401 68 Weekday No a) Which variable is the response? b) Define two dummy variables to recode the “Day of the week” and “Free Samples” columns. c) Fit an MLR equation to the data ( ). Write out the “full” model. d) Is the overall model significant? Justify with ANOVA hypotheses and p-value e) Are the individual variables significant? If not, remove the insignificant variables stepwise, until all remaining variables are significant. Also, check if there are any interactions between temperature and significant dummy variables. f) Write the “best” model you’ve come up with. g) Predict the number of customers the manager should expect on a Saturday with a forecasted high temperature of 80 degrees and an employee scheduled to hand out free samples. h) What is the slope term in the equation for “Temperature” when “Day of the Week” = Weekend? Interpret the meaning of this value in terms of the problem. What is the slope for “Temperature” when “Day of the Week” = Weekday? Interpret the meaning of this value in terms of the problem. i) Is it worth it, for the manager, to pay an employee to stand outside the entrance and give out free samples?